TOKYO, Sept 11 (Reuters) - Japan brushed off warnings byChina and bought a group of islands on Tuesday that both claim,in a growing dispute that threatens ties between Asia's twobiggest economies.

Chinese official media said Beijing had sent two patrolships to waters surrounding the islands to reassert its claimand accused Japan of "playing with fire" over the long-simmeringrow.

Tokyo insisted that it had only peaceful intentions inmaking the 2.05 billion yen ($26.18 million) purchase of threeuninhabited islands in the East China Sea, until now leased bythe government from a Japanese family that has owned them sinceearly 1970s.

"We cannot damage the stable development of the Japan-Chinarelationship because of that issue. Both nations need to actcalmly and from a broad perspective," he told reporters after acabinet meeting approved the transaction.

The Japanese Coast Guard will administer the islands,called Senkaku in Japan and Diaoyu in China, which are near richfishing grounds and potentially huge maritime gas fields.

The long-running territorial dispute flared again last monthafter Japan detained a group of Chinese activists who had landedon the islands.

But the row appears to be having an economic impact, with aChinese official saying Japanese car sales in the world'sbiggest auto market may have been hit.

Chinese President Hu Jintao's warned at the weekend againstthe purchase, which he called "illegal". On Tuesday Taiwan,which also claims the territory recalled its representative toJapan in protest against the deal.

The news triggered small-scale protests in front of thetightly-guarded Japanese embassy in Beijing. Microbloggers onChina's popular Twitter-like service Sina Weibo also reportedsmall anti-Japanese protests in the eastern city of Weihai andthe southwestern city of Chongqing.

Japanese Prime Minister Yoshihiko Noda, in an address tosenior military officers, made no direct reference to theislands dispute, but pointed to China's growing military cloutas one of challenges Japan had to contend with.

"We have North Korea launching missiles under the name ofsatellites and conducting a nuclear programme, China expandingits military might and continuing vigorous activities inregional waters and Russia also boosting its activities in theFar East," Noda said.

The foreign ministry said it is sending its Asia departmentchief to Beijing on Tuesday for talks to "avoid misunderstandingand lack of explanation on the issue."

The government bought three out of five islets that it hasbeen leasing from the Kurihara family, which itself bought theislands in 1972 from another Japanese family that had controlledthem since the 1890s. The government has owned one of theremaining islets and continues to lease one from the Kuriharafamily.

Noda floated the plan to buy the islets in July to head offwhat appeared to be a much more provocative bid by Tokyogovernor Shintaro Ishihara, a harsh critic of China, to purchasethem and make the islands available for development.

But Beijing, at least in public, has repeatedly warnedagainst the government purchase.

On Tuesday, People's Liberation Army Daily said in acommentary that Japan was playing with fire. Xinhua news agencyreported two patrol vessels were heading into waters surroundingthe islands.

The Japanese Coast Guard could not confirm the report.

Relations between the Asian powers, plagued by Japan'swartime occupation of parts of China and present rivalry overregional clout, have been difficult for years. But economic tiesare stronger than ever and both countries are believed to wantto keep the feud from spiralling out of control.